Question

An AC circuit draws 5 A current at 160 V, and the power consumption is 600 W. What is the power factor?
A. 1
B. $0.75$
C. $0.5$
D. Zero

Answer 1

Hint
For DC circuits, there is a direct relationship between voltage and the current. For AC circuits, the phase angle also affects the perceived values of power consumption.
$\Rightarrow P = VI\cos \theta$, where P is the power consumption in an AC circuit, V is the voltage, I is the current, and $\theta$ is the phase angle.

Complete step by step answer
Power factor in an AC circuit is defined as the ratio of the real power that is used to do work and the apparent power that is supplied to the circuit. It also measures the phase angle between instantaneous current and instantaneous voltage. Consequently, its value lies between 0 and 1.
In this question we are asked to determine the power factor when the following details are provided to us:
Type of circuit: AC
Current in Amperes: 5
Voltage in Volts: 160
Power consumption: 600 W
We know that for an AC circuit, the power consumption is given by:
$\Rightarrow P = VI\cos \theta$
Putting the known values in this equation:
$\Rightarrow 600 = 160 \times 5 \times \cos \theta$
Getting the unknown on the LHS:
$\Rightarrow \cos \theta = \dfrac{{600}}{{160 \times 5}} = \dfrac{{600}}{{800}}$
$\Rightarrow \cos \theta = \dfrac{3}{4} = 0.75$
We know that the power factor is equal to $\cos \theta$.
Hence, the correct value for the power factor is given by option (B).

Note
The ideal power factor in any AC circuit is equal to 1. Since it is the ratio of actual power drawn to the power supplied to the circuit, a value less than unity implies that more power is needed to perform the work.